It would not include grocery or convenience stores that don’t serve prepared food and wouldn’t apply to diet soda, other calorie-free drinks or anything that has at least 50 percent milk or milk substitute.

Bloomberg held a separate event Monday promoting the proposal. He said the city’s trans fat ban met with similar resistance but is reducing fat consumption.

The mayor also has the support from the Health Care Workers Union. George Gresham, president of Local 1199, said his 125 member board unanimously approved the measure.

“We as health care workers in particular have seen the results that diabetes has on our community and our patients,” said Gresham.

(TM and Copyright 2012 CBS Radio Inc. and its relevant subsidiaries. CBS RADIO and EYE Logo TM and Copyright 2012 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)